# FIND THE DISTANCE  BETWEEN TWO POINTS USING FORMULA

Let (x1, y1) and (x2, y2) be the two points as shown below. Then, the formula for the distance between the two points is

√[(x2 - x1)2 + (y2 - y1)2]

## Practice Questions

Question 1 :

Find the distance between the following pairs of points.

(1, 2) and (4, 3)

Distance between two points  =  √(x2 - x1)2 + (y2 - y1)2

=  √(4 - 1)2 + (2 - 3)2

=  √32 + (-1)2

=  √(9 + 1)

=  √10

Question 2 :

Find the distance between the following pairs of points.

(3, 4) and (– 7, 2)

Distance between two points  =  √(x2 - x1)2 + (y2 - y1)2

=  √(-7 - 3)2 + (2 - 4)2

=  √(-10)2 + (-2)2

=  √(100 + 4)

=  √104

=  2 √26

Question 3 :

Find the distance between the following pairs of points.

(a, b) and (c, b)

Distance between two points  =  √(x2 - x1)2 + (y2 - y1)2

=  √(c - a)2 + (b - b)2

=  √(c - a)2 + 02

=  (c - a)

Question 4 :

Find the distance between the following pairs of points.

(3, -9) and (-2, 3)

Distance between two points  =  √(x2 - x1)2 + (y2 - y1)2

=  √(-2 - 3)2 + (3 - (-9))2

=  √(-5)2 + (3+9)2

=  √25 + 144

=  √169

=  13

Question 5 :

Determine whether the given set of points in each case are collinear or not.

(7, –2),(5, 1),(3, 4)

Let the given points be A (7, –2) B (5, 1) and C (3, 4)

Distance between the points A and B :

=  √(5 - 7)2 + (1 - (-2))2

=  √(-2)2 + (1+2)2

=  √4 + 9

=  √13

Distance between the points B and C :

=  √(3 - 5)2 + (4 - 1)2

=  √(-2)2 + (3)2

=  √4 + 9

=  √13

Distance between the points C and A :

=  √(3 - 7)2 + (4 - (-2))2

=  √(-4)2 + (6)2

=  √16 + 36

=  √52

=  2√13

√13 + √13  =  2√13

So, the given points are collinear.

Question 6 :

Determine whether the given set of points in each case are collinear or not.

(a, –2), (a, 3), (a, 0)

Let the given points be A (a, –2) B (a, 3) and C (a, 0)

Distance between the points A and B :

=  √(a - a)2 + (3 - (-2))2

=  √0 + (5)2

=  √0 + 25

=  √25

=  5

Distance between the points B and C :

=  √(a - a)2 + (0 - 3)2

=  √(0)2 + (3)2

=  √9

=  3

Distance between the points C and A :

=  √(a - a)2 + (0 - (-2))2

=  √(0)2 + (2)2

=  √4

=  2

BC + CA  =  AB

3 + 2  =  5

5  =  5

So, the given points are collinear. Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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